As many others already stated, there are more than just small subtle differences that will bite you with this approach. Eventually forcing you to develop unnecessary compatibility abstractions or downgrade to less efficient lowest common denominator feature set to make it work. It's not worth the effort.

Especially since launching postgres is equally easy and fast as sqlite. Docker can help with sandboxing. What is left to gain? 100ms shorter startup time or keeping your unit test executables as single binaries? Irrelevant.